Step 1. The expression we have for the graph is:
[tex]6=5x+2y[/tex]
To find the inequality that represents the graph, we need to solve for y first.
Step 2. Solve for y in the equation:
[tex]6=5x+2y[/tex]
We can also represent this as follows:
[tex]5x+2y=6[/tex]
Move 5x to the right side as a -5x:
[tex]2y=-5x+6[/tex]
Move the two that is multiplying on the left side, to divide on the right side:
[tex]y=\frac{-5x+6}{2}[/tex]
Simplify:
[tex]\begin{gathered} y=-\frac{5}{2}x+\frac{6}{2} \\ \downarrow \\ y=-\frac{5}{2}x+3 \end{gathered}[/tex]
This is the equation of the line.
Step 3. Find the inequality.
Since the shaded part is below the line, and it has a dotted line, the inequality that represents this is:
[tex]y<-\frac{5}{2}x+3[/tex]
Which are the values below the dotted line.
Answer:
[tex]y<-\frac{5}{2}x+3[/tex]
